Understanding the movement of ground water near managed aquifer recharge facilities (MAR) and groundwater pump-and-treat (P&T) systems is critical to their safe, efficient and effective operation. Ground water movement can be rapidly evaluated using automated data processing and mapping to depict groundwater pressures throughout one or more aquifers. For instance, hybrid analytic element/geo-statistical methods can be used to condition groundwater pressure interpolations that include source and sink terms such as wells and percolation ponds. Furthermore, Runge-Kutta integration may be used to track the movement of groundwater and/or contaminants within multiple groundwater potentiometric fields near MAR and P&T facilities. An integrated telemetered system of pressure transducers and flow-rate meters can produce piecewise-continuous data to feed such hybrid algorithms to produce hydraulically conditioned potentiometric maps within moments of data collection. In this way, the potentiometric surface computed at a particular time increment incorporates source and sink terms operating at that instant to produce a sequence of conditioned (“calibrated”) potentiometric surfaces that cannot be easily obtained using a numerical model because of the great effort expended to calibrate such numerical models.
Transient potentiometric results have variously been depicted using frequency-based maps. Hybrid interpolation and associated particle tracking algorithms, which may be stationed remotely, on a PC or on a secure website, enable rapid evaluation of P&T and MAR performance. Such methods rely upon kriging variants to interpolate values of a sampled variable to a regular grid suitable for contouring of equivalent groundwater pressures within an aquifer unit or for other purposes. These kriging methods generally use interpolation weights obtained by solving an “event-specific” system of linear equations, which in this context means one system of equations for each time occasion on which sample data are available. For example, universal kriging (UK) incorporates a generalized least-squares (GLS) regression that enables non-stationary variables to be interpolated (“mapped”) using a spatially varying mean based on the underlying physics. A UK equation is constructed by combining physically based trend terms. At sites with multiple data sets, UK can be used to sequentially prepare maps for each monitoring event. Methods have also been described that use this approach to interpolate water level data together with the use of particle tracking to construct a capture frequency map (CFM) to evaluate the performance of a P&T system. However, the use of such methods that map each event independently of all other events implies that (i) trend coefficients calculated for each event are unrelated; (ii) sufficient data exists for each event to estimate the trend coefficients; (iii) residuals from the trend are uncorrelated between events; and, (iv) sufficient data exists for each event to estimate a residual semi-variogram. It is very often the case that one or more of these calculations is violated.
The inventors recognized certain shortcomings with such approaches and herein describe a novel method for formulating and solving the kriging matrix equations to create maps that represent a geospatial area based upon spatio-temporal data sets that encompass multiple disparate times (or events). In particular, the inventors describe a “simultaneous” multi-event universal kriging (MEUK) method that uses spatio-temporal interpolation to create a series of related maps, where each map corresponds to a specific sampling event for the geospatial area, but where at least some features within the maps exhibit spatial relationships that persist over time. MEUK was designed specifically to mathematically address the assumptions noted above by constructing a block-diagonal kriging matrix, the structure of which defines trend term relationships between different monitoring events. Thus, MEUK enables simultaneous conditioning of trend coefficients based on any arbitrary user-defined subset of data or the entirety of a multi-event sample data set, which provides a physically-based, quasi-deterministic basis rather than a wholly-stochastic basis for evaluating and mapping data correlations in space and time. In one example provided, a method for preparing groundwater-pressure elevation maps using MEUK is disclosed that produces mapped potentiometric surfaces that can be used to infer the performance of very complex and costly groundwater P&T systems.
The above advantages and other advantages, and features of the present description will be readily apparent from the following Detailed Description when taken alone or in connection with the accompanying drawings. The summary above is provided to introduce in simplified form a selection of concepts that are further described in the Detailed Description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure.